Standard methods for the analysis of hybrid systems rely on numerical techniques for solving the differential equations and can be unsound on certain classes of hybrid systems. These techniques are susceptible to dimension explosion problems as the number of state variables increases. What has been sought is an approach that is both capable of generating sound abstractions and capable of being compositionally applied.
The application of modeling tools to hybrid qualitative and quantitative systems, including, in particular biological systems, poses significant challenges. A means of providing analytical proofs of the unreachability of certain states, as well as stability and bistability properties of complex systems is sought. This capability is outside the reach of traditional modeling for analysis methods.
Further, what is needed is the ability to reason in an automated or semi-automated manner about biological systems to answer complex questions about the biological relevance of complicated molecular or intercellular signaling or other biochemical reaction networks.